Supersymmetry on a lattice and Dirac fermions in a random vector potential

We study two-dimensional Dirac fermions in a random non-Abelian vector pote ntial by using lattice regularization. We consider U(N) random vector poten tial for large N. The ensemble average with respect to random vector potent ial is taken by using lattice supersymmetry which we introduced before in o rder to investigate phase structure of supersymmetric gauge theory. We show that a phase transition occurs at a certain critical disorder strength. Th e ground state and low-energy excitations are studied in detail in the stro ng-disorder phase. Correlation function of the fermion local density of sta tes decays algebraically at the band center because of a quasi-long-range o rder of chiral symmetry and the chiral anomaly cancellation in the lattice regularization (the species doubling). In the present study, we use the lat tice regularization and also the Haar measure of U(N) for the average over the random vector potential. Therefore topologically nontrivial configurati ons of the vector potential are all included in the average. Implication of the present results for the system of Dirac fermions in a random vector po tential with noncompact Gaussian distribution is discussed. (C) 2000 Elsevi er Science B.V. All rights reserved.